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Slide 1 of 48 Measurements and Their Uncertainty 3.1 3.1

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© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 2 of 48 Significant Figures in Calculations How does the precision of a calculated answer compare to the precision of the measurements used to obtain it? 3.1

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Slide 3 of 48 © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Significant Figures in Calculations In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. The calculated value must be rounded to make it consistent with the measurements from which it was calculated. 3.1

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© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 4 of 48 3.1 Significant Figures in Calculations Rounding To round a number, you must first decide how many significant figures your answer should have. The answer depends on the given measurements and on the mathematical process used to arrive at the answer.

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© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 5 of 48 3.1

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© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 6 of 48 3.1

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© Copyright Pearson Prentice Hall Slide 7 of 48 Practice Problems. for Sample Problem 3.1 Write down your answers.

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© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 8 of 48 3.1 Significant Figures in Calculations Addition and Subtraction The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

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© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 9 of 48 3.2

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© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 10 of 48 12.52 349.0 8.24 369.76 Final Answer 369.8 meters

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© Copyright Pearson Prentice Hall Slide 11 of 48 Practice Problems for Sample Problem 3.2 Write down your answers and round to The correct number of SFs..

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© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 12 of 48 3.1 Significant Figures in Calculations Multiplication and Division In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures. The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.

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© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 13 of 48 3.3

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© Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 14 of 48 3.3

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© Copyright Pearson Prentice Hall Slide 15 of 48 Practice Problems for Sample Problem 3.3 Write down your answer with the correct Number of SFs.

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© Copyright Pearson Prentice Hall Slide 16 of 48 Section Quiz -or- Continue to: Launch: Assess students understanding of the concepts in Section 3.1. Section Assessment Write down your answers.

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© Copyright Pearson Prentice Hall Slide 17 of 48 3.1 Section Quiz 1. In which of the following expressions is the number on the left NOT equal to the number on the right? a.0.00456 10 –8 = 4.56 10 –11 b.454 10 –8 = 4.54 10 –6 c.842.6 10 4 = 8.426 10 6 d.0.00452 10 6 = 4.52 10 9

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© Copyright Pearson Prentice Hall Slide 18 of 48 3.1 Section Quiz 2. Which set of measurements of a 2.00-g standard is the most precise? a.2.00 g, 2.01 g, 1.98 g b.2.10 g, 2.00 g, 2.20 g c.2.02 g, 2.03 g, 2.04 g d.1.50 g, 2.00 g, 2.50 g

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© Copyright Pearson Prentice Hall Slide 19 of 48 3. A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement? a.2 b.3 c.4 d.5 3.1 Section Quiz

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